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To approximate the volume, partition the square $[-2,2] \times [-2,2]$ into four equal subsquares, each with side length 2 and area $\Delta A_k = 2^2 = 4$. Choose a sample point in each subsquare (e.g., the bottom-left corner).

Conditions: The base region is $[-2,2] \times [-2,2]$.; The partition consists of four equal subsquares.; Sample points are chosen according to a specific rule (e.g., bottom-left corners).

To approximate the volume, partition the square $[-2,2] \times [-2,2]$ into four equal subsquares, each with side length 2 and area $\Delta A_k = 2^2 = 4$. Choose a sample point in each subsquare (e.g., the bottom-left corner).

Conditions: The base region is $[-2,2] \times [-2,2]$.; The partition consists of four equal subsquares.; Sample points are chosen according to a specific rule (e.g., bottom-left corners).

The volume is defined by a four-step limiting process. First, partition the rectangular region $[a,b] \times [c,d]$ into small subrectangles with area $\Delta A_k = \Delta x_k \Delta y_k$.

Conditions: The base region must be a rectangle $[a,b] \times [c,d]$.; The function $f(x,y)$ defines the height of the surface.; The limit is taken as the largest subrectangle area approaches zero.

The volume is defined by a four-step limiting process. First, partition the rectangular region $[a,b] \times [c,d]$ into small subrectangles with area $\Delta A_k = \Delta x_k \Delta y_k$.

Conditions: The base region must be a rectangle $[a,b] \times [c,d]$.; The function $f(x,y)$ defines the height of the surface.; The limit is taken as the largest subrectangle area approaches zero.